Is (dr)² equal to dx² + dy² + dz² or (xdx + ydy + zdz)²/(x² + y² + z²)?

[jk22]

I'm confused, Is the value of $(dr)^2$
$$dx^2+dy^2+dz^2$$

Or $$\frac{(xdx+ydy+zdz)^2}{x^2+y^2+z^2}$$

?

 

[member 587159]

What is $r$? If it is $r= \sqrt{x^2 + y^2 + z^ 2}$, then the second option is correct.

 

[jk22]

The first were $(d\vec{r})^2$ ?

 

[member 587159]

Maybe you should tell what all that notation means before asking questions...

 

[fresh_42]

Is $r$ a radius or a metric / distance?

 

[Chestermiller]

I think you meant that $\mathbf{dr}$ is a differential position vector between 2 closely neighboring locations in 3D space. In Cartesian coordinates, $$\mathbf{dr}=\mathbf{i_x}dx+\mathbf{i_y}dy+\mathbf{i_z}dz$$What do you get when you dot this vector with itself?